If one side of a triangle is 10 inches long, which of the following could NOT be the lengths, in inches, of the other sides?
A. 2 & 9
B. 3 & 5
C. 5& 10
D. 10 & 10
E. 10 & 12
I think it might be B but I don't know and I don't know how to figure the answer.. please help!
This is a second post of the same question. I answered it already.
To figure out which lengths could not be the lengths of the other sides of the triangle, we can apply the Triangle Inequality Theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's consider each option and apply the theorem:
A. 2 & 9: The sum of 2 and 9 is 11, which is greater than 10. So, this option satisfies the Triangle Inequality Theorem.
B. 3 & 5: The sum of 3 and 5 is 8, which is greater than 10. So, this option satisfies the Triangle Inequality Theorem.
C. 5 & 10: The sum of 5 and 10 is 15, which is greater than 10. So, this option satisfies the Triangle Inequality Theorem.
D. 10 & 10: The sum of 10 and 10 is 20, which is equal to 10. According to the Triangle Inequality Theorem, the sum of the lengths of any two sides must be greater than the length of the third side. In this case, the lengths are equal and not greater, so this option does not satisfy the Triangle Inequality Theorem.
E. 10 & 12: The sum of 10 and 12 is 22, which is greater than 10. So, this option satisfies the Triangle Inequality Theorem.
Therefore, the option that could not be the lengths of the other sides of the triangle is option D. 10 & 10.